# nncross.pp3

##### Nearest Neighbours Between Two Patterns in 3D

Given two point patterns `X`

and `Y`

in three dimensions,
finds the nearest neighbour in `Y`

of each point of `X`

.

##### Usage

```
# S3 method for pp3
nncross(X, Y,
iX=NULL, iY=NULL,
what = c("dist", "which"),
…,
k = 1,
sortby=c("range", "var", "x", "y", "z"),
is.sorted.X = FALSE,
is.sorted.Y = FALSE)
```

##### Arguments

- X,Y
Point patterns in three dimensions (objects of class

`"pp3"`

).- iX, iY
Optional identifiers, used to determine whether a point in

`X`

is identical to a point in`Y`

. See Details.- what
Character string specifying what information should be returned. Either the nearest neighbour distance (

`"dist"`

), the identifier of the nearest neighbour (`"which"`

), or both.- k
Integer, or integer vector. The algorithm will compute the distance to the

`k`

th nearest neighbour.- sortby
Determines which coordinate to use to sort the point patterns. See Details.

- is.sorted.X, is.sorted.Y
Logical values attesting whether the point patterns

`X`

and`Y`

have been sorted. See Details.- …
Ignored.

##### Details

Given two point patterns `X`

and `Y`

in three dimensions,
this function finds, for each point of `X`

,
the nearest point of `Y`

. The distance between these points
is also computed.
If the argument `k`

is specified, then the `k`

-th nearest
neighbours will be found.

The return value is a data frame, with rows corresponding to
the points of `X`

. The first column gives the nearest neighbour
distances (i.e. the `i`

th entry is the distance
from the `i`

th point of `X`

to the nearest element of
`Y`

). The second column gives the indices of the nearest
neighbours (i.e.\ the `i`

th entry is the index of
the nearest element in `Y`

.)
If `what="dist"`

then only the vector of distances is returned.
If `what="which"`

then only the vector of indices is returned.

The argument `k`

may be an integer or an integer vector.
If it is a single integer, then the `k`

-th nearest neighbours
are computed. If it is a vector, then the `k[i]`

-th nearest
neighbours are computed for each entry `k[i]`

. For example, setting
`k=1:3`

will compute the nearest, second-nearest and
third-nearest neighbours. The result is a data frame.

Note that this function is not symmetric in `X`

and `Y`

.
To find the nearest neighbour in `X`

of each point in `Y`

,
use `nncross(Y,X)`

.

The arguments `iX`

and `iY`

are used when
the two point patterns `X`

and `Y`

have some points in
common. In this situation `nncross(X, Y)`

would return some zero
distances. To avoid this, attach a unique integer identifier to
each point, such that two points are identical if their
identifying numbers are equal. Let `iX`

be the vector of
identifier values for the points in `X`

, and `iY`

the vector of identifiers for points in `Y`

. Then the code
will only compare two points if they have different values of the
identifier. See the Examples.

##### Value

A data frame, or a vector if the data frame would contain only one column.

By default (if `what=c("dist", "which")`

and `k=1`

)
a data frame with two columns:

Nearest neighbour distance

Nearest neighbour index in `Y`

If what="dist" and k=1, a vector of nearest neighbour distances.

If what="which" and k=1, a vector of nearest neighbour indices.

If k is specified, the result is a data frame with columns containing the k-th nearest neighbour distances and/or nearest neighbour indices.

##### Sorting data and pre-sorted data

Read this section if you care about the speed of computation.

For efficiency, the algorithm sorts both
the point patterns `X`

and `Y`

into increasing order of the \(x\) coordinate,
or both into increasing order of the \(y\) coordinate,
or both into increasing order of the \(z\) coordinate.
Sorting is only an intermediate step;
it does not affect the output, which is always given in the same
order as the original data.

By default (if `sortby="range"`

),
the sorting will occur on the coordinate that has the largest range of
values (according to the frame of the enclosing window of `Y`

).
If `sortby = "var"`

), sorting will occur on the coordinate that
has the greater variance (in the pattern `Y`

).
Setting `sortby="x"`

or `sortby = "y"`

or `sortby = "z"`

will specify that
sorting should occur on the \(x\), \(y\) or \(z\) coordinate,
respectively.

If the point pattern `X`

is already
sorted, then the corresponding argument `is.sorted.X`

should be set to `TRUE`

, and `sortby`

should be set
equal to `"x"`

, `"y"`

or `"z"`

to indicate which coordinate
is sorted.

Similarly if `Y`

is already sorted, then `is.sorted.Y`

should be set to `TRUE`

, and `sortby`

should be set
equal to `"x"`

, `"y"`

or `"z"`

to indicate which coordinate
is sorted.

If both `X`

and `Y`

are sorted *on the same coordinate
axis* then both `is.sorted.X`

and `is.sorted.Y`

should be set to `TRUE`

, and `sortby`

should be set
equal to `"x"`

, `"y"`

or `"z"`

to indicate which coordinate
is sorted.

##### See Also

`nndist`

for nearest neighbour
distances in a single point pattern.

##### Examples

```
# NOT RUN {
# two different point patterns
X <- pp3(runif(10), runif(10), runif(10), box3(c(0,1)))
Y <- pp3(runif(20), runif(20), runif(20), box3(c(0,1)))
N <- nncross(X,Y)$which
N <- nncross(X,Y, what="which") #faster
# note that length(N) = 10
# k-nearest neighbours
N3 <- nncross(X, Y, k=1:3)
# two patterns with some points in common
Z <- pp3(runif(20), runif(20), runif(20), box3(c(0,1)))
X <- Z[1:15]
Y <- Z[10:20]
iX <- 1:15
iY <- 10:20
N <- nncross(X,Y, iX, iY, what="which")
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*